STAT 495, Fall 2004
Homework Assignment #6
1. In the manufacture of computer components wafers containing 50 chips are made. The location of
chips on a wafer is measured for 30 wafers. A defective chip is defined whenever a mis-registration, in
terms of vertical and/or horizontal distance from the center, is recorded. The data appear below. The
data can also be obtained from the course web page.
Wafer
Number
1
2
3
4
5
6
7
8
9
10
Number
Defective
12
15
8
10
4
7
16
9
14
10
Wafer
Number
11
12
13
14
15
16
17
18
19
20
Number
Defective
5
6
17
12
22
8
10
5
13
11
Wafer
Number
21
22
23
24
25
26
27
28
29
30
Number
Defective
20
18
24
15
9
12
7
13
9
6
(a) Calculate the average number defective for the 30 wafers and use this to compute the limits for
an np control chart. Do these calculations by hand.
(b) Use JMP or Minitab to actually construct the np chart.
(c) Are there any wafers that plot outside control limits? If so, which wafers are they and what are
the associated number of defective chips?
(d) If special causes are found for the wafers identified in c) and those special causes removed, how
will the centerline and control limits change on the np chart?
2. At an automobile assembly plant, body sides are attached to the underbody at a particular assembly
station. A fault (defective car) occurs whenever both body sides are unable to be placed on the car
properly. Below are the number of cars built and the number of faults for each of 50 day’s production.
Of the 24,317 cars built there are 1,652 faults (defective cars). The data is also available on the course
web page.
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Cars
484
445
482
476
511
504
535
517
453
479
514
509
443
453
494
Faults
43
44
33
42
43
47
33
51
18
38
28
17
24
29
38
Day
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Cars
512
422
406
477
497
522
516
470
441
504
506
477
468
470
486
Faults
28
21
30
25
45
13
21
34
21
32
31
31
49
36
26
Day
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Cars
518
500
469
507
530
517
497
478
126
453
495
474
530
506
489
Faults
36
30
52
33
26
26
25
34
34
28
30
45
42
35
31
Day
46
47
48
49
50
Cars
496
501
474
497
487
(a) What are the center line and control limits for the p control chart for Day 1?
1
Faults
28
13
59
43
31
(b) Use JMP or Minitab to construct the p control chart.
(c) Are there any days that plot outside the control limits? If so, what days are they and what are
the associated fractions defective?
(d) If special causes are found for the days that plot outside the control limits would you want to
eliminate those special causes? Explain briefly.
3. For the data in problem 2, the plant manager is interested in whether the number of good cars (Cars
- Faults) is in a state of statistical control.
(a) What is the average number of good cars built per day?
(b) Use your answer in a) to calculate c control chart limits for the number of good cars built per
day. Do this calculation by hand.
(c) Use JMP or Minitab to construct the c control chart for the number of good cars built.
(d) Are there any days that plot outside control limits? If so, what days are they and how many good
cars were built on those days?
2